Release Time:2019-03-09  Hits:

Indexed by: Journal Papers

Date of Publication: 2015-12-01

Journal: MATHEMATICAL METHODS IN THE APPLIED SCIENCES

Included Journals: Scopus、EI、SCIE

Volume: 38

Issue: 18,SI

Page Number: 5048-5062

ISSN: 0170-4214

Key Words: homoclinic orbit; fountain theorem; dual fountain theorem; damped differential equation

Abstract: We investigate the existence and multiplicity of homoclinic orbits for the second- order damped differential equations
   u+g(t)u - L(t)u +W-u(t,u) =0,
   where L(t) and W(t, u) are neither autonomous nor periodic in t. Under certain assumptions on g, L, andW, we get infinitely many homoclinic orbits for superquadratic, subquadratic and concave-convex nonlinearities cases by using fountain theoremand dual fountain theoremin critical point theory. These results generalize and improve some existing results in the literature. Copyright (C) 2015 JohnWiley & Sons, Ltd.